Can't access my songs on iTunes

Question

I recently had my laptop fixed and all of my music was saved and re-downloaded into iTunes. Now when I go into my iTunes I have 2 issues.. for some reason there are doubles of A LOT of my songs. And only some of my songs will play, the others tell me "You don't have authorization to play this on your computer, authorize now?"
When I do the authorization using my aol account it tells me I have to use my Apple ID instead, so I use that... It goes through and tells me I have authorized this computer. When I click on the song again.. It tells me I'm not authorized. I went through the FAQs and tried using some of the steps they mentioned to authorize my computer, but it still doesn't work.
I really would love to update my iPod, but if all these songs won't play in my iTunes.. I'm afraid they'll be deleted off my iPod, and that would be in the HUNDREDS.
Please help, and thank you very much for your time.

Answer 1

Thank you both for your suggestions but neither worked. I tried every step they offered. Here's what it tells me:
I click the "song" and go to "file"--> "get info"
There it tells me my account name which was originally used, it was my aol screen name. So I go to "store"--> "authorize computer"
I enter my aol name and password it then tells me:
"*You need to change your account to use an Apple ID*"
But I have already done that, ages ago.. Years ago, so I tried authorizing using my apple ID and it still won't work.
I just keep getting repeated authorization prompts, even after removing SC info and restarting.